Reinforcing Moving Linear Model Approach: Theoretical Assessment of Parameter Estimation and Outlier Detection

This paper reinforces the previously proposed moving linear (ML) model approach for time series analysis by introducing theoretically grounded enhancements. The ML model flexibly decomposes a time series into constrained and remaining components, enabling the extraction of trends and fluctuations with minimal structural assumptions. Building on this framework, we present two key improvements. First, we develop a theoretically justified evaluation criterion that facilitates coherent estimation of model parameters, particularly the width of the time interval. Second, we enhance the extended ML (EML) model by introducing a new outlier detection and estimation method that identifies both the number and locations of outliers by maximizing the reduction in AIC. Unlike the earlier version, the reinforced EML model simultaneously estimates outlier effects and improves model fit within a unified, likelihood-based framework. Empirical applications to economic time series illustrate the method’s superior ability to detect meaningful anomalies and produce stable, interpretable decompositions. These contributions offer a generalizable and theoretically supported approach to modeling nonstationary time series with structural disturbances.